Question: $f(x) = -3x^{2}+3$ What is the range of $f(x)$ ?
Answer: Consider the range of $-3x^{2}$ The range of $x^2$ is $\{\, y \mid y \ge 0 \,\}$ Multiplying by $-3$ flips the range to $\{\, y \mid y \le 0 \,\}$ To get $-3x^{2}+3$, we add $3$.